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A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its q-analogue based on the Askey--Wilson polynomials. On the top, it has two-index biorthogonal functions formed from elliptic hypergeometric series with the absolutely continuous measure determined by the elliptic beta integral. A new result is an inclusion of complex hypergeometric functions into the scheme. Its further potential generalizations are discussed as well.
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V. P. Spiridonov (Sun,) studied this question.
synapsesocial.com/papers/68e72a6ab6db6435876a419e — DOI: https://doi.org/10.48550/arxiv.2403.16264
V. P. Spiridonov
National Research University Higher School of Economics
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